Model theory of a Hilbert space expanded with an unbounded closed selfadjoint operator

We study a closed unbounded self‐adjoint operator Q acting on a Hilbert space H in the framework of Metric Abstract Elementary Classes (MAECs). We build a suitable MAEC for such a structure, prove it is ?₀‐categorical and ?₀‐stable up to a system of perturbations. We give an explicit continuous axiomatization for the class. We also characterize non‐splitting and show it has the same properties as non‐forking in superstable first order theories. Finally, we characterize equality, orthogonality and domination of (Galois) types in that MAEC.     

A first-order block-decomposition method for solving two-easy-block structured semidefinite programs

In this paper, we consider a first-order block-decomposition method for minimizing the sum of a convex differentiable function with Lipschitz continuous gradient, and two other proper closed convex (possibly, nonsmooth) functions with easily computable resolvents. The method presented contains two important ingredients from a computational point of view, namely: an adaptive choice of stepsize for performing an extragradient step; and the use of a scaling factor to balance the blocks. We then specialize the method to the context of conic semidefinite programming (SDP) problems consisting of two easy blocks of constraints. Without putting them in standard form, we show that four important classes of graph-related conic SDP problems automatically possess the above two-easy-block structure, namely: SDPs for $\theta $ -functions and $\theta _{+}$ -functions of graph stable set problems, and SDP relaxations of binary integer quadratic and frequency assignment problems. Finally, we present computational results on the aforementioned classes of SDPs showing that our method outperforms the three most competitive codes for large-scale conic semidefinite programs, namely: the boundary point (BP) method introduced by Povh et al., a Newton-CG augmented Lagrangian method, called SDPNAL, by Zhao et al., and a variant of the BP method, called the SPDAD method, by Wen et al.     

The model theory of modules of a C*-algebra

We study the theory of a Hilbert space H as a module for a unital C*-algebra ${\mathcal{A}}$ from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are elementary equivalent to it. Also, we show that this theory has quantifier elimination and we characterize the model companion of the incomplete theory of all non-degenerate representations of ${\mathcal{A}}$ . Finally, we show that there is an homeomorphism between the space of types of norm less than 1 in this model companion, and the space of quasistates of the C*-algebra ${\mathcal{A}}$ .     

Microwave-assisted synthesis of 2-aminonicotinic acids by reacting 2-chloronicotinic acid with amines

2-(Methylamino)nicotinic acid was readily prepared in high yield by reacting 2-chloronicotinic acid with 40% aq MeNH₂ under microwave irradiation either at 120 °C for 2 h or at 140 °C for 1.5 h. Subsequently, we found that a range of 2-aminonicotinic acids could be obtained under microwave heating. The optimal reaction conditions involved the use of 3 equiv of amine, water as the solvent and heating at 200 °C for 2 h in the presence of diisopropylethylamine (3 equiv).     

Lithium ionization by a strong laser field

We study ab initio computations of the interaction of lithium with a strong laser field. Numerical solutions of the time-dependent fully correlated three-particle Schrodinger equation restricted to the one-dimensional soft-core approximation are presented. Our results show a clear transition from nonsequential to sequential double ionization for increasing intensities. Nonsequential double ionization is found to be sensitive to the spin configuration of the ionized pair. This asymmetry, also found in experiments of photoionization of Li with synchrotron radiation, shows evidence of the influence of the exclusion principle on the underlying rescattering mechanism.     

The thermal isomerization of 6-difluoromethylenebicyclo[3.2.0]hept-2-ene

The thermal isomerization of 6-difluoromethylenebicyclo[3.2.0]hept-2-ene proceeds via two competing 1,3-sigmatropic processes, with an E_a nearly identical to that of the hydrocarbon.     

Charge accumulation kinetics in multi-redox molecular catalysts immobilised on TiO2

Multi-redox catalysis requires the accumulation of more than one charge carrier and is crucial for solar energy conversion into fuels and valuable chemicals. In photo(electro)chemical systems, however, the necessary accumulation of multiple, long-lived charges is challenged by recombination with their counterparts. Herein, we investigate charge accumulation in two model multi-redox molecular catalysts for proton and CO₂ reduction attached onto mesoporous TiO₂ electrodes. Transient absorption spectroscopy and spectroelectrochemical techniques have been employed to study the kinetics of photoinduced electron transfer from the TiO₂ to the molecular catalysts in acetonitrile, with triethanolamine as the hole scavenger. At high light intensities, we detect charge accumulation in the millisecond timescale in the form of multi-reduced species. The redox potentials of the catalysts and the capacity of TiO₂ to accumulate electrons play an essential role in the charge accumulation process at the molecular catalyst. Recombination of reduced species with valence band holes in TiO₂ is observed to be faster than microseconds, while electron transfer from multi-reduced species to the conduction band or the electrolyte occurs in the millisecond timescale. Finally, under light irradiation, we show how charge accumulation on the catalyst is regulated as a function of the applied bias and the excitation light intensity.

Using transient spectroelectrochemical techniques, we investigate multiply reduced states of molecular catalysts on titania photoelectrodes as a function of the applied bias and the light intensity.     

Thermal elimination of diethyldithiocarbamates and application in the synthesis of (+/-)-ferrugine

Dithiocarbamate-substituted lactams, prepared through group-transfer cyclization reactions of carbamoyl radicals, undergo a Chugaev-like thermal elimination of the dithiocarbamate group in refluxing diphenyl ether to form alpha,beta- and/or beta,gamma-unsaturated amides, depending on the structure of the starting material. This reaction sequence was used to prepare an unsaturated [3.2.2] bridged bicyclic amide, which was converted in a one-pot procedure to the 8-azabicyclo[3.2.1]octane ring system of the tropane alkaloid ferrugine by treatment with phenyllithium followed by aqueous sodium hydroxide.     

On higher-dimensional Courant algebroids

We define the transgression functor which associates with a (higher-dimensional) Courant algebroid on a manifold a Lie algebroid on the shifted tangent bundle of the manifold.